Title:
The open flux evolution of a solar-mass star on the main sequence

Abstract: Magnetic activity is known to be correlated to the rotation period for
moderately active main sequence solar-like stars. In turn, the stellar rotation
period evolves as a result of magnetised stellar winds that carry away angular
momentum. Understanding the interplay between magnetic activity and stellar
rotation is therefore a central task for stellar astrophysics. Angular momentum
evolution models typically employ spin-down torques that are formulated in
terms of the surface magnetic field strength. However, these formulations fail
to account for the magnetic field geometry, unlike those that are expressed in
terms of the open flux, i.e. the magnetic flux along which stellar winds flow.
In this work, we model the angular momentum evolution of main sequence
solar-mass stars using a torque law formulated in terms of the open flux. This
is done using a potential field source surface model in conjunction with the
Zeeman-Doppler magnetograms of a sample of roughly solar-mass stars. We explore
how the open flux of these stars varies with stellar rotation and choice of
source surface radii. We also explore the effect of field geometry by using two
methods of determining the open flux. The first method only accounts for the
dipole component while the second accounts for the full set of spherical
harmonics available in the Zeeman-Doppler magnetogram. We find only a small
difference between the two methods, demonstrating that the open flux, and
indeed the spin-down, of main sequence solar-mass stars is likely dominated by
the dipolar component of the magnetic field.